Process capability indices estimation

The critical characteristic on each component was analysed, calculated from the analysis and the value obtained was plotted against the process capability indices, Cpk and Cp, for the characteristic in question. See Appendix V for descriptions of the 21 components analysed, including the values of Cp and Cp from the SPC data supplied. Note that some components studied have a zero process capability index. This is a default value given if the process capability index calculated from the SPC data had a mean outside either one of the tolerance limits, which was the case for some of the components submitted. Although it is recognized that negative process capability indices are used for the aim of process improvement, they have little use in the analyses here. A correlation between positive values (or values which are at least within the tolerance limits) will yield a more deterministic relationship between design capability and estimated process capability. 

A standard for the minimum acceptable process capability index for any component/characteristic is normally set at = 1.33, and this standard will be used later to align costs of failure estimates. If the characteristics follow a Normal distribution, Cp = 1.33 corresponds to a fault probability of ... 

The process capability index, Cpk, is related to the so-called process sigma such that a 6a process corresponds to a Cpk of exactly 2.00, or 2.0 defective parts per billion (PPB), assuming N (0, a) quality variance distribution (can alternative calculation for process sigma estimates 3.4 defective parts per million for a 6a process). Examples of the correspondence between Cpk, process sigma, and defect rate for N(0, a) distributions are shown in Figure 2. The process capability (based on observed yield) of pharmaceutical manufacturers has been cited by some benchmark studies to be roughly 0.7 (2.1a) [28]. 

It is important to remember that the capability and performance indices calculated from the data are only estimates and thus have uncertainty associated with them. Confidence intervals can be calculated for these indices to reflect this imprecision. For example, a 100(1 — a)% two-sided confidence interval about the estimated process capability index Cp is ... 

The process capability index (Cpk) was estimated to determine the ability of the process to meet design objectives. Based on last 450 observations, the Cpk was estimated to be 1.77 and is shown in Figure 14. 

The goal is the analysis of risks, determination of MP(2I and failure probabilities of manufacturing processes based on multivariate product characteristics. Subsequently, it is possible to ensure optimised manufacturing processes. This paper focuses on one method for the calculation of multidimensional process capability index with an analogy to the state-of-the-art PCI. An overview of the developed method regarding the estimation of Multivariate Process Capability Indices (MPCI) is shown in Figure 1. The method steps are theoretically explained and applied within the case study in the following sections. 

The expression allows the direct conversion of an estimated failure probability into a value. Based on this conversion (direct link), the estimation of a multivariate process capability index MPCI is feasible The estimation of the expected failure probability with regard to the combination of two or more important product characteristics is shown in section 6.2, Table 2. 

Dow Fire and Explosion Index. The Dow Eire and Explosion Index (3) is a procedure usehil for determining the relative degree of hazard related to flammable and explosive materials. This Index form works essentially the same way as an income tax form. Penalties are provided for inventory, extended temperatures and pressures, reactivity, etc, and credits are appHed for fire protection systems, process control (qv), and material isolation. The complete procedure is capable of estimating a doUar amount for the maximum probable property damage and the business intermptionloss based on an empirical correlation provided with the Index. 

Use of the Cp estimate assumes that the process is centered at or near the exact middle of the specification range of a two-sided specification. This represents the best capability achievable. The Cpk estimate assesses the process with no assumption that the process is centered, and this estimate is always equal to or less than the corresponding Cp estimate. If the distribution of the output is close to a normal distribution and the capability index is based on a large and representative sample size, then acceptance values can be established. Some industries define a process with Cp = 1 as barely capable and one with Cpk = 1-33 or higher as capable. (Note that a CpK = 1 represents a situation where the process is centered and the specification range is equal to 6dc)... 

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